Equation 677 Database

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Magma 0c1ac17e2fe4…

magma 0c1ac17e2fe4
Size
705
Isomorphism class hash
0c1ac17e2fe4c61b0d02ec915f36e2e343f242bb9513da4c6ef4253d2013272a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:25:12
Display reorder
660,89,634,629,631,628,654,648,87,649,651,614,608,88,609,611,548,554,85,549,551,568,574,86,569,571,588,594,84,589,591,447,452,95,448,449,469,476,93,470,472,429,436,94,430,432,516,509,91,510,512,534,528,92,529,531,496,489,90,490,492,693,701,694,691,47,620,622,635,632,641,652,45,642,655,600,612,46,602,615,552,540,43,542,555,572,561,44,562,575,592,581,42,582,595,451,443,38,444,453,474,462,36,463,477,434,421,37,423,437,500,514,41,503,517,520,533,39,522,535,481,494,40,483,497,696,699,702,698,176,322,346,298,274,323,275,174,347,299,321,273,175,345,297,270,318,179,342,294,271,319,177,343,295,272,320,178,344,296,265,313,171,337,289,266,314,172,338,290,264,312,173,336,288,316,268,170,340,292,317,269,168,341,293,315,267,169,339,291,666,664,663,661,146,14,4,334,418,12,419,144,5,335,13,417,145,3,333,414,17,149,1,330,415,15,147,0,331,416,16,148,2,332,409,20,152,10,325,410,18,150,11,326,408,19,151,9,324,23,412,155,6,328,21,413,153,7,329,22,411,154,8,327,676,673,665,678,180,638,633,627,639,658,659,181,653,647,618,619,182,613,607,559,558,183,553,547,579,578,184,573,567,599,598,185,593,587,458,459,186,450,446,478,479,187,473,468,438,439,188,433,428,519,518,189,513,508,539,538,190,532,527,499,498,191,493,488,697,692,690,687,255,630,626,621,624,650,644,256,646,640,610,604,257,606,601,544,550,254,546,541,564,570,252,566,560,584,590,253,586,580,456,457,261,441,440,465,471,262,467,460,425,431,263,427,420,511,505,260,507,501,530,524,258,526,521,491,485,259,487,480,689,686,695,700,24,637,625,636,623,656,643,25,645,657,617,603,26,605,616,543,557,27,545,556,563,577,28,565,576,583,596,29,585,597,454,455,30,445,442,464,475,31,466,461,424,435,32,426,422,515,504,33,506,502,537,523,34,525,536,495,484,35,486,482,688,703,704,685,58,217,200,382,208,218,209,59,198,383,216,207,57,199,381,204,220,54,203,378,205,221,55,201,379,206,219,56,202,380,214,223,49,195,373,215,224,50,196,374,213,222,48,197,372,226,210,52,194,376,227,211,53,192,377,225,212,51,193,375,672,679,669,674,74,394,276,370,406,395,407,72,277,371,393,405,73,278,369,402,390,77,279,366,403,391,75,280,367,404,392,76,281,368,397,385,80,282,361,398,386,78,283,362,396,384,79,284,360,388,400,83,285,364,389,401,81,286,365,387,399,82,287,363,682,670,668,671,163,121,97,143,306,122,307,164,98,141,120,308,162,96,142,309,124,166,100,139,310,125,167,101,140,311,123,165,99,138,304,127,161,103,134,305,128,159,104,132,303,126,160,102,133,130,300,157,106,137,131,301,158,107,135,129,302,156,105,136,683,681,677,684,111,241,358,68,232,242,233,112,359,66,240,231,113,357,67,228,244,110,354,71,229,245,108,355,69,230,243,109,356,70,238,247,117,349,63,239,248,118,350,64,237,246,119,348,65,250,234,116,352,62,251,235,114,353,60,249,236,115,351,61,667,662,680,675 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#198f8683bee40b5fe0cfed42350fb71daef6a15506139cdcf5a71dcf11978025, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 15:25:13 · history